The scope trials: Variation in sensitivity to scope and WTP with directionally bounded utility functions
Introduction
The controversy over the use of the contingent valuation (CV) method has focused on various tests of validity and reliability. One test that has received much attention is the “scope test”, which examines whether estimated willingness to pay (WTP) is sensitive to the scope of the good being valued. As pointed out by Hanemann [4] in his review of the CV method, studies that explicitly consider the scope issue date back to the 1970s. The issue received increasing attention when Kahneman [6] suggested a scope test, and provided an example where the scope test failed. Kahneman compared estimates of demand for cleaning up all lakes in Ontario with estimates for two subregions, and showed that the estimates were similar. Kahneman concluded that willingness to pay was not adequately sensitive to the scope of the good. Such results have been used to cast doubt on the validity or reliability of CV studies. Subsequently, numerous CV studies have applied the scope test [3], [4], [5].
In most CV studies that include a scope test, statistically significant sensitivity to scope is in fact found. In a review of CV studies that include a scope test, Carson [3] found that roughly 80 percent show positive sensitivity to scope. While this suggests that CV studies frequently pass the scope test, two controversies remain. First, there is the issue of the roughly 20 percent of studies that fail to meet the test. As stated by Heberlein et al. [5, p. 2] “Where would the theory of gravity be if one out of five rocks when dropped landed on the ceiling? Theoretical validity would obviously be thrown into serious doubt.” A second concern has to do with whether the degree of sensitivity to scope is sufficient in magnitude in cases where it is positive. Even when the measured sensitivity to scope is statistically significant, is it economically significant? To borrow the Heberlein metaphor, for those rocks that drop, do they fall at a sufficient rate? Is the magnitude of the effect consistent with neoclassical consumer theory, or do we need to look for some alternative explanation?
The first of these controversies is examined by Herberlein et al. [5]. It may be that studies finding an absence of sensitivity to scope simply suffer from poor survey design or implementation. A different explanation may be applicable to some cases. Using the above metaphor [5, p. 2], asks whether some of the rocks fail to drop because they are not rocks at all, but rather “helium balloons cleverly disguised as rocks”, in which case their failure to drop does not invalidate the theory of gravity. The authors consider the scope test for four different types of environmental goods. Based on a reconsideration of the goods in question, and using a more careful analysis of social psychology than typically accompanies scope tests, the authors conclude that we might expect to observe zero, or even negative, sensitivity to scope in some cases.
In this paper we examine the second controversy. For those cases where we would expect to find positive sensitivity to scope, might a low degree of sensitivity be consistent with rational consumer behavior? The importance of this issue was highlighted in the NOAA report on contingent valuation, which suggests that “Inadequate responsiveness to the scope of the environmental insult” in a CV study represents grounds to “judge its findings ‘unreliable’ ” [2, p. 63]. What constitutes “inadequate responsiveness”? We examine this issue formally in the context of neoclassical consumer theory. We show that there is a broad class of utility functions that is consistent with arbitrarily small degrees of sensitivity to scope. Utility functions of this type—which we refer to as directionally bounded utility functions—satisfy all of the axioms of neoclassical consumer theory, including non-satiation. With these functions, all goods are continuously substitutable at the margin, but there are non-local restrictions on substitution. These properties allow for arbitrarily small degrees of sensitivity to scope for any set of discrete changes. We show that this further complicates the interpretation of scope tests and conclude that a simple scope test, as traditionally applied, does not reveal much about the reliability of CV studies. We emphasize that our results do not imply that any particular CV study (or set of studies) is valid or reliable, or has demonstrated adequate sensitivity to scope. A review of the circumstances and validity or reliability of existing studies is not the goal of our analysis. Rather, our focus is on evaluating the theoretical validity of the scope test itself.
Section snippets
Utility functions and substitution
Willingness to pay (WTP) for an environmental amenity depends on the substitutability of market goods for the environmental amenity. In real terms, payment involves giving up claims on market goods in exchange for an additional increment of the amenity. The willingness of a consumer to substitute the environmental amenity for the foregone market goods depends on the nature of the consumer's utility function.
Some commonly used utility functions impose rather extreme assumptions regarding
Sensitivity to scope and bounded substitution
As noted in the Introduction, many empirical studies of willingness to pay find that WTP increases only slowly as the scope of a good expands. For example, in comparing the public's willingness to pay for a given increment of wildlife habitat, , to a larger increment , it is often found that WTP for the larger increment is not much higher than for the smaller increment. While studies usually find that WTP does rise as the quantity of the good increases (that is, the “sensitivity to scope”
Summary and conclusions
Tests of sensitivity to scope have received considerable attention in the assessment of contingent valuation studies. Two issues have arisen in this context. First, in some cases, there is no statistically significant change in estimated willingness to pay as the scope of the good is expanded. Second, in many cases the change in willingness to pay is statistically significant, but the degree of sensitivity to scope is very small, which raises questions as to whether it is economically
Acknowledgments
The authors thank the referees and editors for their many useful comments.
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